Find the acceleration of C with respect to th | vedclass

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Question

(A) Let the acceleration of $C$ be $\vec{a}_C = c_x \hat{i} + c_y \hat{j}$.Block $A$ moves with acceleration $a$ in the $+x$ direction,so $c_x = a$.Us

Vedclass · Accepted Answer

$a \hat{i}-(2 a+2 b) \hat{j}$

Vedclass · Answer

(A) Let the acceleration of $C$ be $\vec{a}_C = c_x \hat{i} + c_y \hat{j}$.Block $A$ moves with acceleration $a$ in the $+x$ direction,so $c_x = a$.Using the constraint motion for the string connected to block $A$ and block $B$ (which moves with acceleration $b$ in the $-x$ direction),the total length of the string remains constant.Let the positions of the pulleys be such that the vertical segments of the string are affected by the relative motion of $A$ and $B$.The vertical acceleration $c_y$ of block $C$ is determined by the constraint equation: $c_y = 2a + 2b$ in the downward direction.Thus,in the ground frame,the acceleration of $C$ is $\vec{a}_C = a \hat{i} - (2a + 2b) \hat{j}$.

Find the acceleration of $C$ with respect to the ground.

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